Mensuration Quantitative Aptitude Questions

1) Three sides of a triangular field are 20 metres, 21 metres and 29 metres long respectively. The area of the field is?
(A) 200 m2
(B) 210 m2
(C) 290 m2
(D) 300 m2

View Answer

Answer: Option B

Solution:
Here S =
20+21+29/2

=
70/2
=> 35m
Area = √(35(35-20) (35-21)(35-29)
= √35*15*14*6
= √52 * 72 * 32 * 22
= 210 m2

2) The area of a triangular lawn is 1600 sq m. If one side is 64 m long and the other two sides are equal in length, the length of each equal side is
(A) 58.36
(B) 60.26
(C) 59.36
(D) 60.37

View Answer

Answer: Option C

Solution:
Let the length of equal sides be x.
Then S =
x + x + 64/2
= x + 32
Area = 1600 sq metres
= √(x+32)(x+32-x)(x+32-x)(x+32-64)
= √(x+32)*32*32*(x-32)
or 1600 = 32 √x2 - 322
√x2 - 322 = 50
or x2 = 322 + 502 = 1024 + 2500 = 3524
x = 59.36 metres

3) The length of each side of a triangle is 12 cm. The height of the triangle is
(A) 6 √2cm
(B) 3 √2cm
(C) 6 √3cm
(D) 8 √3cm

View Answer

Answer: Option C

Solution:
Each side = 12cm
Then S = 12+12+12/2 = 18
Area = √18*6*6*6 =
1/2
* 12 * Height
or height =
36√3/6

= 6√3 cm

4) The length of a rectangle is thrice its breadth and its perimeter is 96 m. The area of the rectangle is
(A) 288 sq. m
(B) 442sq. m
(C) 438sq. m
(D) 432 sq. m

View Answer

Answer: Option D

Solution:
Let the width of the rectangle be x metre
Then length = 3x metre
Perimeter = 2(x + 3x) = 96 => 8x = 96
or x = 12
Area = 12*36 = 432 sq.metres

5) If the sides of a rectangle are increased by 30% the percentage increase in its area is
(A) 90
(B) 29
(C) 69
(D) 60

View Answer

Answer: Option C

Solution:
Let the length = L metre and the width = B metre
Then, Area = L*B sq. metres
Increased length =
130/100
L = 1.3L
Increased width =
130/100
B = 1.3B
Increased Area = 1.69LB or % increase = 69%

6) A wheel revolves 1254 times in travelling a distance of 2 km 5 hectometer and 8 meters. The circumference of the wheel is
(A) 2 m
(B) 3 m
(C) 5 m
(D) 6 m

View Answer

Answer: Option A

Solution:
Total distance traveled by wheel = 2000 + 500 + 8 = 2508 m
As this distance traveled in 1254 revolutions the distance distance traveled in one revolution =
2508/1254
= 2 metres
The circumference of the wheel is the distance traveled in 1 revolution i.e 2 metres


7) The external dimensions of a wooden box are 18 cm, 10 cm and 6 cm and thickness of the wood is 0.5 cm. The volume of the box is
(A) 780 cm3
(B) 765 cm3
(C) 914 cm3
(D) 1080 cm3

View Answer

Answer: Option B

Solution:
Internal dimensions of the box are (18 - 1)cm, (10 - 1)cm and (6 - 1)cm
i.e , 17, 9 and 5 cm
Volume of the box = 17*9*5 cm3
= 765 cm3

8) A sphere of radius 0.12 m is melted and out of the metal a fine wire of radius 1 millimetre is drawn out. The length of the wire will be
(A) 2300 m
(B) 2304 m
(C) 2400 m
(D) 2404 m

View Answer

Answer: Option B

Solution:
Radius of the sphere = 0.12 metre = 12 cm
Volume of the sphere =
4/3
π * 123 cm3
If the length of the wire is L cm, then
4/3
π * 123 = π(0.1)2 * L
or L =
4/3
*
123/(0.1)3
=
4*12*12*12/3*0.1*0.1*0.1

= 2304 * 103 cm
= 2304 metres

Quantitative

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